Time-dependent reliability of aging structures in the presence of non-stationary loads and degradation Quanwang Li a,⇑ , Cao Wang a , Bruce R. Ellingwood b,c a Department of Civil Engineering, Tsinghua University, Beijing, China b TNList, Tsinghua University, Beijing, China c Department of Civil and Environmental Engineering, Colorado State University, Ft. Collins, CO, USA article info Article history: Received 26 May 2014 Received in revised form 13 October 2014 Accepted 14 October 2014 Available online 18 November 2014 Keywords: Loads (forces) Probability Time-dependent reliability Structural aging Non-stationary load Auto-covariance in resistance abstract Civil infrastructure performance and reliability may be affected by deterioration in strength or stiffness caused by service or environmental conditions or by systemic changes in load beyond the baseline conditions assumed for design. These changes should be considered when assessing a structure for its continued future reliability in service. This paper presents an improved method for evaluating time- dependent reliability of structures taking these factors into account. The method enables the impact on safety and serviceability of non-stationarity in the load and resistance deterioration processes to be assessed quantitatively. Parametric analyses show that the reliability is sensitive to the load intensity at the end of the service period, moderately sensitive to the initial and final mean occurrence rates of load events and the nature of these increases in time, and relatively insensitive to the nature of the increase in mean load intensity. A realistic time-dependent model of structural resistance is proposed and the role played by the auto-covariance in the resistance degradation process is investigated. The auto-covariance in stochastic resistance plays a significant role in time-dependent reliability assessment. Assuming that the time-dependent resistance is ‘fully correlated’ generally gives a reasonable estimation of structural reliability, while assuming that the resistances are statistically independent at two points in time may cause the failure probability to be overestimated. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Civil infrastructure may suffer from severe operating or envi- ronmental conditions in service. Such conditions may cause changes in strength and stiffness of structures beyond the baseline conditions assumed for their design. Structural deterioration may impair the safety and serviceability of structures, and should be considered when evaluating their fitness for continued service, a process which must provide quantitative evidence that they can withstand future extreme events with an acceptable level of reli- ability during their future service lives. There are many classes of buildings and other constructed facilities for which degradation in service is either known or believed to have an impact on structural safety. Due to socio-eco- nomic constraints, many degraded structures are still in use. Much research has been conducted in the past two decades on the safety evaluation and damage assessment of existing structures [17,18,9,11,2,23,5,12,24,14,22]. Many factors, including environ- mental conditions, variation in load intensity over time, and quality of periodic maintenance may affect the structural degradation pro- cess. However, the exact influence of these factors can be difficult to predict. Because of this time-dependent behavior and the presence of uncertainties, the safety evaluation and service-life prediction of deteriorating structures should be based on reliability concepts and methods, considering the time-dependent characteristics of both the load and resistance [8]. The methodology developed by Mori and Ellingwood [17] was one of the first attempts to assess time- dependent reliability of structures considering both the random- ness of resistance and the stochastic nature of load, and was used to predict the remaining service-life of deteriorating concrete struc- tures [10,12,18]. However, Mori and Ellingwood assumed that while the initial resistance was random, the time-dependent func- tion describing resistance degradation was deterministic. Thus, the stochastic nature of time-dependent resistance deterioration was not considered in their work. In addition, Mori and Ellingwood trea- ted the loads during the service life as a stationary random process consisting of a sequence of identically distributed and statistically independent loads, with a constant mean occurrence rate over the service life of the structure. Such stationary load models are unreal- istic in many cases. For example, live load studies for highway http://dx.doi.org/10.1016/j.strusafe.2014.10.003 0167-4730/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Structural Safety 52 (2015) 132–141 Contents lists available at ScienceDirect Structural Safety journal homepage: www.elsevier.com/locate/strusafe